{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# linear_programming"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/examples/linear_programming.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/examples/python/linear_programming.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "Linear programming examples that show how to use the APIs.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.linear_solver import pywraplp\n",
    "\n",
    "\n",
    "def Announce(solver, api_type):\n",
    "    print(\n",
    "        \"---- Linear programming example with \" + solver + \" (\" + api_type + \") -----\"\n",
    "    )\n",
    "\n",
    "\n",
    "def RunLinearExampleNaturalLanguageAPI(optimization_problem_type):\n",
    "    \"\"\"Example of simple linear program with natural language API.\"\"\"\n",
    "    solver = pywraplp.Solver.CreateSolver(optimization_problem_type)\n",
    "\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    Announce(optimization_problem_type, \"natural language API\")\n",
    "\n",
    "    infinity = solver.infinity()\n",
    "    # x1, x2 and x3 are continuous non-negative variables.\n",
    "    x1 = solver.NumVar(0.0, infinity, \"x1\")\n",
    "    x2 = solver.NumVar(0.0, infinity, \"x2\")\n",
    "    x3 = solver.NumVar(0.0, infinity, \"x3\")\n",
    "\n",
    "    solver.Maximize(10 * x1 + 6 * x2 + 4 * x3)\n",
    "    c0 = solver.Add(10 * x1 + 4 * x2 + 5 * x3 <= 600, \"ConstraintName0\")\n",
    "    c1 = solver.Add(2 * x1 + 2 * x2 + 6 * x3 <= 300)\n",
    "    sum_of_vars = sum([x1, x2, x3])\n",
    "    c2 = solver.Add(sum_of_vars <= 100.0, \"OtherConstraintName\")\n",
    "\n",
    "    SolveAndPrint(\n",
    "        solver, [x1, x2, x3], [c0, c1, c2], optimization_problem_type != \"PDLP\"\n",
    "    )\n",
    "    # Print a linear expression's solution value.\n",
    "    print(\"Sum of vars: %s = %s\" % (sum_of_vars, sum_of_vars.solution_value()))\n",
    "\n",
    "\n",
    "def RunLinearExampleCppStyleAPI(optimization_problem_type):\n",
    "    \"\"\"Example of simple linear program with the C++ style API.\"\"\"\n",
    "    solver = pywraplp.Solver.CreateSolver(optimization_problem_type)\n",
    "    if not solver:\n",
    "        return\n",
    "\n",
    "    Announce(optimization_problem_type, \"C++ style API\")\n",
    "\n",
    "    infinity = solver.infinity()\n",
    "    # x1, x2 and x3 are continuous non-negative variables.\n",
    "    x1 = solver.NumVar(0.0, infinity, \"x1\")\n",
    "    x2 = solver.NumVar(0.0, infinity, \"x2\")\n",
    "    x3 = solver.NumVar(0.0, infinity, \"x3\")\n",
    "\n",
    "    # Maximize 10 * x1 + 6 * x2 + 4 * x3.\n",
    "    objective = solver.Objective()\n",
    "    objective.SetCoefficient(x1, 10)\n",
    "    objective.SetCoefficient(x2, 6)\n",
    "    objective.SetCoefficient(x3, 4)\n",
    "    objective.SetMaximization()\n",
    "\n",
    "    # x1 + x2 + x3 <= 100.\n",
    "    c0 = solver.Constraint(-infinity, 100.0, \"c0\")\n",
    "    c0.SetCoefficient(x1, 1)\n",
    "    c0.SetCoefficient(x2, 1)\n",
    "    c0.SetCoefficient(x3, 1)\n",
    "\n",
    "    # 10 * x1 + 4 * x2 + 5 * x3 <= 600.\n",
    "    c1 = solver.Constraint(-infinity, 600.0, \"c1\")\n",
    "    c1.SetCoefficient(x1, 10)\n",
    "    c1.SetCoefficient(x2, 4)\n",
    "    c1.SetCoefficient(x3, 5)\n",
    "\n",
    "    # 2 * x1 + 2 * x2 + 6 * x3 <= 300.\n",
    "    c2 = solver.Constraint(-infinity, 300.0, \"c2\")\n",
    "    c2.SetCoefficient(x1, 2)\n",
    "    c2.SetCoefficient(x2, 2)\n",
    "    c2.SetCoefficient(x3, 6)\n",
    "\n",
    "    SolveAndPrint(\n",
    "        solver, [x1, x2, x3], [c0, c1, c2], optimization_problem_type != \"PDLP\"\n",
    "    )\n",
    "\n",
    "\n",
    "def SolveAndPrint(solver, variable_list, constraint_list, is_precise):\n",
    "    \"\"\"Solve the problem and print the solution.\"\"\"\n",
    "    print(\"Number of variables = %d\" % solver.NumVariables())\n",
    "    print(\"Number of constraints = %d\" % solver.NumConstraints())\n",
    "\n",
    "    result_status = solver.Solve()\n",
    "\n",
    "    # The problem has an optimal solution.\n",
    "    assert result_status == pywraplp.Solver.OPTIMAL\n",
    "\n",
    "    # The solution looks legit (when using solvers others than\n",
    "    # GLOP_LINEAR_PROGRAMMING, verifying the solution is highly recommended!).\n",
    "    if is_precise:\n",
    "        assert solver.VerifySolution(1e-7, True)\n",
    "\n",
    "    print(\"Problem solved in %f milliseconds\" % solver.wall_time())\n",
    "\n",
    "    # The objective value of the solution.\n",
    "    print(\"Optimal objective value = %f\" % solver.Objective().Value())\n",
    "\n",
    "    # The value of each variable in the solution.\n",
    "    for variable in variable_list:\n",
    "        print(\"%s = %f\" % (variable.name(), variable.solution_value()))\n",
    "\n",
    "    print(\"Advanced usage:\")\n",
    "    print(\"Problem solved in %d iterations\" % solver.iterations())\n",
    "    for variable in variable_list:\n",
    "        print(\"%s: reduced cost = %f\" % (variable.name(), variable.reduced_cost()))\n",
    "    activities = solver.ComputeConstraintActivities()\n",
    "    for i, constraint in enumerate(constraint_list):\n",
    "        print(\n",
    "            (\n",
    "                \"constraint %d: dual value = %f\\n               activity = %f\"\n",
    "                % (i, constraint.dual_value(), activities[constraint.index()])\n",
    "            )\n",
    "        )\n",
    "\n",
    "\n",
    "def main():\n",
    "    RunLinearExampleNaturalLanguageAPI(\"GLOP\")\n",
    "    RunLinearExampleNaturalLanguageAPI(\"GLPK_LP\")\n",
    "    RunLinearExampleNaturalLanguageAPI(\"CLP\")\n",
    "    RunLinearExampleNaturalLanguageAPI(\"PDLP\")\n",
    "\n",
    "    RunLinearExampleCppStyleAPI(\"GLOP\")\n",
    "    RunLinearExampleCppStyleAPI(\"GLPK_LP\")\n",
    "    RunLinearExampleCppStyleAPI(\"CLP\")\n",
    "    RunLinearExampleCppStyleAPI(\"PDLP\")\n",
    "\n",
    "\n",
    "main()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
